What is 71/20 as a Decimal?
71/20 = 3.55
Step by step
- Simplify: 71/20 is already in simplest form
- Divide the numerator by the denominator: 71 ÷ 20 = 3.55
How the answer is worked out
A fraction is a division: 71/20 means 71 divided by 20, and doing that division gives 3.55. The division ends after a few digits, because the simplified denominator has no prime factors other than 2 and 5.
As a percentage, 71/20 is 355%. It is an improper fraction: as a mixed number it is 3 11/20.
Why calculate this?
Decimals are easier to compare and to use in calculators and spreadsheets than fractions.
- Cooking: a recipe that asks for 71/20 of a cup needs 3.55 cups, about 852 millilitres.
- Measuring: 71/20 of an inch is 3.55 inches, or 90.17 millimetres.
- Money: 71/20 of a dollar is about $3.55, and 71/20 of $100 is $355.
A quicker way
The simplified denominator 20 divides 100, so scale the fraction up instead of dividing: 71/20 = 355/100 = 3.55.
Check the answer
Work backwards: 3.55 × 20 = 71, which is 71 once rounding is allowed for.
Rounding
Rounded to a whole number the decimal is 4, to one decimal place 3.5 and to two decimal places 3.55. Round only at the end: rounding halfway through a calculation can change the last digit.
The formula explained
decimal = numerator ÷ denominator. The numerator is the top number and counts the pieces; the denominator is the bottom number and says how many equal pieces make a whole. Dividing the top by the bottom gives the size of the fraction as a decimal.
Another worked example: 14/94 as a decimal
- Simplify: 14/94 = 7/47 (divide by 2)
- Divide the numerator by the denominator: 14 ÷ 94 = 0.14893617
- The digits in brackets repeat forever: 0.(1489361702127659574468085106382978723404255319)
Equivalent fractions
71/20 has the same value as 142/40, 213/60 and 710/200: multiplying the top and bottom by the same number never changes a fraction. All of them give 3.55 when divided out.
Comparing with nearby fractions
71/20 (3.55) is bigger than 71/21 (3.381) and smaller than 72/20 (3.6). A bigger denominator means smaller pieces, so with the same numerator the fraction gets smaller.
The reciprocal
Flipping the fraction gives 20/71 = 0.(28169014084507042253521126760563380). A number multiplied by its reciprocal is always 1: 71/20 × 20/71 = 1.
In time and money
71/20 of an hour is 213 minutes, and 71/20 of a day is 85.2 hours.
In a pie chart
A slice worth 71/20 of the whole takes up 1,278 degrees of the circle, because a full turn is 360 degrees. That is the angle to draw when you make the chart by hand with a protractor.
Other ways to ask this
The same calculation is often asked in other words. All of these have the answer above:
- 71/20 in decimal form
- 71 divided by 20
- Convert 71 over 20 to a decimal
- What is 71 ÷ 20?
- 71 out of 20 as a decimal number
Terms used on this page
- Numerator: the top number of a fraction.
- Denominator: the bottom number, the number of equal parts in a whole.
- Terminating decimal: a decimal that ends, such as 0.25.
- Repeating decimal: a decimal whose digits repeat forever, such as 0.333….
The answer in other forms
| Decimal | 3.55 |
|---|---|
| Percentage | 355% |
| Simplified | 71/20 |
| Type | improper fraction |
Related results
| 1/20 as a decimal | 1/20 = 0.05 |
| 2/20 as a decimal | 2/20 = 0.1 |
| 3/20 as a decimal | 3/20 = 0.15 |
| 72/20 as a decimal | 72/20 = 3.6 |
| 70/20 as a decimal | 70/20 = 3.5 |
The other way round: 20/71 as a decimal
Doing it in a spreadsheet
In Excel, Google Sheets or Numbers type =71/20 into any cell. Replace the numbers with cell references (for example A1 and B1) to reuse the formula for a whole column.
Common mistakes
Dividing the denominator by the numerator flips the fraction. A bar over (or brackets around) digits means they repeat forever.
Practice examples
| 14/94 as a decimal | Show answer14/94 = 0.(1489361702127659574468085106382978723404255319) |
| 19/95 as a decimal | Show answer19/95 = 0.2 |
| 35/36 as a decimal | Show answer35/36 = 0.97(2) |
| 94/13 as a decimal | Show answer94/13 = 7.(230769) |
| 62/54 as a decimal | Show answer62/54 = 1.(148) |
| 19/22 as a decimal | Show answer19/22 = 0.8(63) |
| 22/81 as a decimal | Show answer22/81 = 0.(271604938) |
| 55/91 as a decimal | Show answer55/91 = 0.(604395) |
| 58/60 as a decimal | Show answer58/60 = 0.9(6) |
| 24/79 as a decimal | Show answer24/79 = 0.(3037974683544) |
How this answer was calculated
The result is worked out from the numbers in this page's address when the page is opened, using exact arithmetic wherever possible and rounding only for display. Nothing is copied from a printed table. If you think an answer is wrong, please tell us through the contact page and we will check it.
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Questions
What is 71/20 as a Decimal?
71/20 as a decimal is 3.55. Long-division steps and simplified fraction.
What is 71/20 as a percentage?
355%. Multiply the decimal 3.55 by 100.
What is 71/20 in simplest form?
71/20 is already in simplest form: 71 and 20 have no common factor other than 1.
Is 71/20 a terminating or a repeating decimal?
Terminating: it stops at 3.55.
What is 71/20 rounded to two decimal places?
3.55. Rounded to three places it is 3.550.
What is 71/20 of 100?
355. Multiply 100 by 71 and divide by 20, or multiply 100 by the decimal 3.55.
What is 71/20 as a ratio?
71:20. A ratio compares the part with the whole in the same way the fraction does.